Question

The coordinates of the endpoints of overline QR are Q(4,18) and R(16,6). Point S is on overline QR and divides it such that QS:RS is 3:1. What are the coordinates of S? Write your answers as integers or decimals. a. (9, 13) b. (13,9)

c. (18, 6)
d. (4, 16)

Answer 1

The coordinates of point S that divides line segment QR in the ratio of 3:1 are (13, 9) using the section formula in coordinate geometry. Option B is correct.

Step-by-step explanation:

The question asks us to find the coordinates of point S on line segment QR such that the ratio of QS:RS is 3:1.

We use the section formula in coordinate geometry to find the point dividing a line segment in a given ratio. The formula for a point P(x, y) that divides the line segment joining A(x1, y1) and B(x2, y2) in the ratio m:n is:

P(x, y) = ((mx2 + nx1) / (m + n), (my2 + ny1) / (m + n))

In this case, we have Q(4, 18), R(16, 6), and the ratio 3:1. Applying the section formula, point S would be:

S = ((3*16 + 1*4) / (3 + 1), (3*6 + 1*18) / (3 + 1))
= ((48 + 4) / 4, (18 + 18) / 4)
= (52 / 4, 36 / 4)
= (13, 9).

So, the coordinates of point S are (13, 9).